The interplay between charge-density-wave (CDW) order and superconductivity (SC) in the Kagome metal RbV3Sb5 is studied by tracking the evolutions of their transition temperatures, T* and Tc, as a function of pressure (P) via measurements of resistivity and magnetic susceptibility under various hydrostatic pressures up to ~ 5 GPa. It is found that the CDW order at T* experiences a subtle modification at Pc1 ~ 1.5 GPa before it is completely suppressed around Pc2 ~ 2.4 GPa. Accordingly, the superconducting transition Tc(P) exhibits a shallow M-shaped double superconducting dome with two extrema of Tconset ~ 4.4 K and 3.9 K around Pc1 and Pc2, respectively, leading to a fourfold enhancement of Tc with respect to that at ambient pressure. The constructed T-P phase diagram of RbV3Sb5 resembles that of CsV3Sb5, and shares similar features as many other unconventional superconducting systems with intertwined competing electronic orders. The strong competition between CDW and SC is also evidenced by the broad superconducting transition width in the coexistent region. Our results shed more light on the intriguing physics involving intertwined electronic orders in this novel topological kagome metal family.
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